{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13.2. Simulating a Poisson process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "rate = 20.  # average number of events per second"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = .001  # time step\n",
    "n = int(1. / dt)  # number of time steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.zeros(n)\n",
    "x[np.random.rand(n) <= rate * dt] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.,  0.,  ...,  0.,  0.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x71a3b38>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x71a3b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 2))\n",
    "ax.vlines(np.nonzero(x)[0], 0, 1)\n",
    "ax.set_axis_off()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x7243940>"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xZa1Hjx5Z3fvuu+/GihUrUtaPO+64dtXU0v3z589v174AAAAAQHHKeMZgqWAQ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\nggUL4vzzz0+homzvv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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7243940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
    "ax.plot(np.linspace(0., 1., n),\n",
    "        np.cumsum(x), lw=2)\n",
    "ax.set_xlabel(\"Time\")\n",
    "ax.set_ylabel(\"Counting process\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.cumsum(np.random.exponential(1. / rate,\n",
    "                                    size=int(rate)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.021,  0.072,  0.087,  0.189,  0.224,\n",
       "        0.365,  0.382,  0.392,  0.458,  0.489])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "podoc": {
     "output_text": "<matplotlib.figure.Figure at 0x736de80>"
    }
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x736de80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 3))\n",
    "ax.vlines(y, 0, 1)\n",
    "ax.set_axis_off()"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 2
}
